A robust technique for the estimation of the two-parameter Weibull function for complete data sets

In this work, a procedure for the calculation of the parameters of a probability distribution function, which is both accurate and robust, is described. This procedure, belonging to the family of regressive methods, is based on a "non-parametric" methodology that employs the percentiles of the distribution of the parameter estimates. This statistical procedure is applied to obtain the point estimates of the two parameters of a Weibull distribution function, which is able to describe effectively the experimental results of complete life tests performed on solid dielectric insulation. Unbiasing factors for the scale and shape parameters of the Weibull function are obtained resorting to the Monte Carlo method. The accuracy and the robustness of the proposed non parametric method are checked by comparison with the other techniques employed in the literature, that is, the Maximum-Likelihood Estimate (MLE), the Least- Square Regression (LSR) and Weighted Least-Square Regression (WLSR) techniques. It is shownthat the methodology proposed here for the estimation of the parameters of the 2- parameter Weibull function is able to provide accurate and robust estimates, particularly useful for samples of data presenting outliers.